Centered Dodecagonal Number

Last Updated : 20 May, 2022

Given a number n, find the nth Centered Dodecagonal Number.
The Centered Dodecagonal Number represents a dot in the center and other dots surrounding it in successive dodecagonal(12 sided polygon) layers.
Examples :

Input :  3
Output : 37

Input : 7
Output :253

centered dodecagonal number

The first few centered dodecagonal numbers are:
1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661.......................
The formula for the nth Centered dodecagonal number:

CDg_{n}= 6n(n-1)+1

C++

// C++ Program to find
// nth centered
// Dodecagonal number
#include <bits/stdc++.h>
using namespace std;

// Function to calculate Centered
// Dodecagonal number
int centeredDodecagonal(long int n)
{
    // Formula to calculate nth
    // centered Dodecagonal number
    return 6 * n * (n - 1) + 1;
}

// Driver Code
int main()
{
    long int n = 2;
    cout << centeredDodecagonal(n);
    cout << endl;
    n = 9;
    cout << centeredDodecagonal(n);

    return 0;
}

// C Program to find
// nth centered
// Dodecagonal number
#include <stdio.h>

// Function to calculate Centered
// Dodecagonal number
int centeredDodecagonal(long int n)
{
    // Formula to calculate nth
    // centered Dodecagonal number
    return 6 * n * (n - 1) + 1;
}

// Driver Code
int main()
{
    long int n = 2;
    printf("%d\n",centeredDodecagonal(n));

    n = 9;
    printf("%d\n",centeredDodecagonal(n));

    return 0;
}

// This code is contributed by kothavvsaakash.

Java

// Java Program to find nth 
// centered dodecagonal number
import java.io.*;

class GFG{
    
// Function to calculate
// centered dodecagonal number
static long centeredDodecagonal(long n)
{
    
    // Formula to calculate nth
    // centered dodecagonal number
    return 6 * n * (n - 1) + 1;
}

// Driver Code
public static void main(String[] args)
{
    long n = 2;
    System.out.println(centeredDodecagonal(n));

    n = 9;
    System.out.println(centeredDodecagonal(n));
}
}

// This code is contributed by anuj_67

Python3

# Python3 program to find nth 
# centered dodecagonal number 

# Function to calculate 
# centered dodecagonal number 
def centeredDodecagonal(n) :
    
    # Formula to calculate nth 
    # centered dodecagonal number 
    return 6 * n * (n - 1) + 1; 

# Driver code
n = 2
print(centeredDodecagonal(n));

n = 9
print(centeredDodecagonal(n)); 

# This code is contributed by grand_master

// C# Program to find nth 
// centered dodecagonal number
using System;
class GFG{

// Function to calculate
// centered dodecagonal number
static long centeredDodecagonal(long n)
{
    
    // Formula to calculate nth
    // centered dodecagonal number
    return 6 * n * (n - 1) + 1;
}

// Driver Code
public static void Main(String[] args) 
{ 
    long n = 2;
    Console.WriteLine(centeredDodecagonal(n));
    
    n = 9;
    Console.WriteLine(centeredDodecagonal(n));
}
}

// This code is contributed by shivanisinghss2110

JavaScript

<script>

// Javascript Program to find
// nth centered
// Dodecagonal number

// Function to calculate Centered
// Dodecagonal number
function centeredDodecagonal(n)
{

    // Formula to calculate nth
    // centered Dodecagonal number
    return 6 * n * (n - 1) + 1;
}

// Driver Code
let n = 2;
document.write(centeredDodecagonal(n));
document.write("<br>");
n = 9;
document.write(centeredDodecagonal(n));

// This code is contributed by rishavmahato348.
</script>

Output :

13
433

Time Complexity: O(1)
Auxiliary Space: O(1)
References
http://oeis.org/A003154

Centered dodecahedral number

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